Geodesic
On the existence of a solution for a periodic boundary value problem for semilinear fractional-order differential inclusions in Banach spaces
Vestnik rossijskih universitetov. Matematika, Tome 26 (2021) no. 135, pp. 250-270

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In this paper, we study a periodic boundary value problem for a class of semilinear differential inclusions of fractional order in a Banach space for which the multivalued nonlinearity satisfies the regularity condition expressed in terms of measures of noncompactness. To prove the existence of solutions to the problem, we first construct the corresponding Green function. Then we introduce into consideration a multivalued resolving operator in the space of continuous functions and reduce the posed problem to the existence of fixed points of the resolving multioperator. To prove the existence of a fixed point, a generalized theorem of B.N. Sadovskii type for a condensing multivalued map is used.
Keywords: differential inclusion, fractional derivative, Green's function, condensing multioperator, measure of noncompactness, fixed point. 
@article{VTAMU_2021_26_135_a3,
     author = {M. I. Kamenskii and V. V. Obukhovskii and G. Petrosyan},
     title = {On the existence of a solution for a periodic boundary value problem for semilinear fractional-order differential inclusions in {Banach} spaces},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {250--270},
     publisher = {mathdoc},
     volume = {26},
     number = {135},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2021_26_135_a3/}
}
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M. I. Kamenskii; V. V. Obukhovskii; G. Petrosyan. On the existence of a solution for a periodic boundary value problem for semilinear fractional-order differential inclusions in Banach spaces. Vestnik rossijskih universitetov. Matematika, Tome 26 (2021) no. 135, pp. 250-270. http://geodesic.mathdoc.fr/item/VTAMU_2021_26_135_a3/